1SORGBR(1) LAPACK routine (version 3.1) SORGBR(1)
2
6 SORGBR - one of the real orthogonal matrices Q or P**T determined by
7 SGEBRD when reducing a real matrix A to bidiagonal form
8
10 SUBROUTINE SORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
11 CHARACTER VECT
13 INTEGER INFO, K, LDA, LWORK, M, N
15 REAL A( LDA, * ), TAU( * ), WORK( * )
17
19 SORGBR generates one of the real orthogonal matrices Q or P**T deter‐
20 mined by SGEBRD when reducing a real matrix A to bidiagonal form: A = Q
21 * B * P**T. Q and P**T are defined as products of elementary reflec‐
22 tors H(i) or G(i) respectively.
23 If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q is of
25 order M:
26 if m >= k, Q = H(1) H(2) . . . H(k) and SORGBR returns the first n col‐
27 umns of Q, where m >= n >= k;
28 if m < k, Q = H(1) H(2) . . . H(m-1) and SORGBR returns Q as an M-by-M
29 matrix.
30 If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T is
32 of order N:
33 if k < n, P**T = G(k) . . . G(2) G(1) and SORGBR returns the first m
34 rows of P**T, where n >= m >= k;
35 if k >= n, P**T = G(n-1) . . . G(2) G(1) and SORGBR returns P**T as an
36 N-by-N matrix.
37
40 VECT (input) CHARACTER*1
41 Specifies whether the matrix Q or the matrix P**T is required,
42 as defined in the transformation applied by SGEBRD:
43 = 'Q': generate Q;
44 = 'P': generate P**T.
45 M (input) INTEGER
47 The number of rows of the matrix Q or P**T to be returned. M
48 >= 0.
49 N (input) INTEGER
51 The number of columns of the matrix Q or P**T to be returned.
52 N >= 0. If VECT = 'Q', M >= N >= min(M,K); if VECT = 'P', N >=
53 M >= min(N,K).
54 K (input) INTEGER
56 If VECT = 'Q', the number of columns in the original M-by-K
57 matrix reduced by SGEBRD. If VECT = 'P', the number of rows in
58 the original K-by-N matrix reduced by SGEBRD. K >= 0.
59 A (input/output) REAL array, dimension (LDA,N)
61 On entry, the vectors which define the elementary reflectors,
62 as returned by SGEBRD. On exit, the M-by-N matrix Q or P**T.
63 LDA (input) INTEGER
65 The leading dimension of the array A. LDA >= max(1,M).
66 TAU (input) REAL array, dimension
68 (min(M,K)) if VECT = 'Q' (min(N,K)) if VECT = 'P' TAU(i) must
69 contain the scalar factor of the elementary reflector H(i) or
70 G(i), which determines Q or P**T, as returned by SGEBRD in its
71 array argument TAUQ or TAUP.
72 WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
74 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
75 LWORK (input) INTEGER
77 The dimension of the array WORK. LWORK >= max(1,min(M,N)). For
78 optimum performance LWORK >= min(M,N)*NB, where NB is the opti‐
79 mal blocksize.
80 If LWORK = -1, then a workspace query is assumed; the routine
82 only calculates the optimal size of the WORK array, returns
83 this value as the first entry of the WORK array, and no error
84 message related to LWORK is issued by XERBLA.
85 INFO (output) INTEGER
87 = 0: successful exit
88 < 0: if INFO = -i, the i-th argument had an illegal value
89 LAPACK routine (version 3.1) November 2006 SORGBR(1)